ces from the centre of the planet. And thence it follows, that the
gravity tending towards all the planets is proportional to the matter
which they contain.

"Moreover, since all the parts of any planet A gravitates towards any
other planet B; and the gravity of every part is to the gravity of the
whole as the matter of the part is to the matter of the whole; and to
every action corresponds a reaction; therefore the planet B will, on the
other hand, gravitate towards all the parts of planet A, and its gravity
towards any one part will be to the gravity towards the whole as the
matter of the part to the matter of the whole. Q.E.D.

"HENCE IT WOULD APPEAR THAT the force of the whole must arise from the
force of the component parts."

Newton closes this remarkable Book iii. with the following words:

"Hitherto we have explained the phenomena of the heavens and of our sea
by the power of gravity, but have not yet assigned the cause of
this power. This is certain, that it must proceed from a cause that
penetrates to the very centre of the sun and planets, without suffering
the least diminution of its force; that operates not according to
the quantity of the surfaces of the particles upon which it acts (as
mechanical causes used to do), but according to the quantity of solid
matter which they contain, and propagates its virtue on all sides to
immense distances, decreasing always in the duplicate proportions of
the distances. Gravitation towards the sun is made up out of the
gravitations towards the several particles of which the body of the sun
is composed; and in receding from the sun decreases accurately in the
duplicate proportion of the distances as far as the orb of Saturn, as
evidently appears from the quiescence of the aphelions of the planets;
nay, and even to the remotest aphelions of the comets, if those
aphelions are also quiescent. But hitherto I have not been able to
discover the cause of those properties of gravity from phenomena, and I
frame no hypothesis; for whatever is not deduced from the phenomena
is to be called an hypothesis; and hypotheses, whether metaphysical or
physical, whether of occult qualities or mechanical, have no place in
experimental philosophy.... And to us it is enough that gravity does
really exist, and act according to the laws which we have explained, and
abundantly serves to account for all the motions of the celestial bodies
and of our sea."(2)

The very magnitude of the im